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          算法学习指南
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        <h2 id="初级"><a href="#初级" class="headerlink" title="初级"></a>初级</h2><h3 id="基本算法"><a href="#基本算法" class="headerlink" title="基本算法"></a>基本算法</h3><ul>
<li>枚举 (poj1753,poj2965)</li>
<li>贪心 (poj1328,poj2109,poj2586)</li>
<li>递归和分治法</li>
<li>递推</li>
<li>构造法 (poj3295)</li>
<li>模拟法 (poj1068,poj2632,poj1573,poj2993,poj2996)</li>
</ul>
<h3 id="图算法"><a href="#图算法" class="headerlink" title="图算法"></a>图算法</h3><ul>
<li>图的深度优先遍历和广度优先遍历</li>
<li>最短路径算法 (dijkstra,bellman-ford,floyd,heap+dijkstra) (poj1860,poj3259,poj1062,poj2253,poj1125,poj2240)</li>
<li>最小生成树算法 (prim,kruskal) (poj1789,poj2485,poj1258,poj3026)</li>
<li>拓扑排序 (poj1094)</li>
<li>二分图的最大匹配(匈牙利算法) (poj3041,poj3020)</li>
<li>最大流的增广路算法(KM算法) (poj1459,poj3436)</li>
</ul>
<h3 id="数据结构"><a href="#数据结构" class="headerlink" title="数据结构"></a>数据结构</h3><ul>
<li>串 (poj1035,poj3080,poj1936)</li>
<li>排序(快排、归并排(与逆序数有关)、堆排) (poj2388,poj2299)</li>
<li>简单并查集的应用</li>
<li>哈希表和二分查找等高效查找法(数的Hash,串的Hash) (poj3349,poj3274,POJ2151,poj1840,poj2002,poj2503)</li>
<li>哈夫曼树 (poj3253)</li>
<li>堆</li>
<li>trie树(静态建树、动态建树) (poj2513)</li>
</ul>
<h3 id="简单搜索"><a href="#简单搜索" class="headerlink" title="简单搜索"></a>简单搜索</h3><ul>
<li>深度优先搜索 (poj2488,poj3083,poj3009,poj1321,poj2251)</li>
<li>广度优先搜索 (poj3278,poj1426,poj3126,poj3087.poj3414)</li>
<li>简单搜索技巧和剪枝 (poj2531,poj1416,poj2676,1129)</li>
</ul>
<h3 id="动态规划"><a href="#动态规划" class="headerlink" title="动态规划"></a>动态规划</h3><ul>
<li>背包问题 (poj1837,poj1276)</li>
<li>型如下表的简单DP(可参考lrj的书 page149)</li>
<li>E[j]=opt{D[i]+w(i,j)} (poj3267,poj1836,poj1260,poj2533)</li>
<li>E[i,j]=opt{D[i-1,j]+xi,D[i,j-1]+yj,D[i-1][j-1]+zij} (最长公共子序列) (poj3176,poj1080,poj1159)</li>
<li>C[i,j]=w[i,j]+opt{C[i,k-1]+C[k,j]} (最优二分检索树问题)</li>
</ul>
<h3 id="数学"><a href="#数学" class="headerlink" title="数学"></a>数学</h3><ul>
<li>组合数学</li>
<li>加法原理和乘法原理</li>
<li>排列组合</li>
<li>递推关系 (POJ3252,poj1850,poj1019,poj1942)</li>
<li>数论</li>
<li>素数与整除问题</li>
<li>进制位</li>
<li>同余模运算 (poj2635, poj3292,poj1845,poj2115)</li>
<li>计算方法</li>
<li>二分法求解单调函数相关知识 (poj3273,poj3258,poj1905,poj3122)</li>
</ul>
<h3 id="计算几何学"><a href="#计算几何学" class="headerlink" title="计算几何学"></a>计算几何学</h3><ul>
<li>几何公式.</li>
<li>叉积和点积的运用 (如线段相交的判定,点到线段的距离等) (poj2031,poj1039)</li>
<li>多边型的简单算法(求面积)和相关判定 (点在多边型内,多边型是否相交) (poj1408,poj1584)</li>
<li>凸包 (poj2187,poj1113)</li>
</ul>
<hr>
<h2 id="中级"><a href="#中级" class="headerlink" title="中级"></a>中级</h2><h3 id="基本算法-1"><a href="#基本算法-1" class="headerlink" title="基本算法"></a>基本算法</h3><ul>
<li>C++的标准模版库的应用 (poj3096,poj3007)</li>
<li>较为复杂的模拟题的训练 (poj3393,poj1472,poj3371,poj1027,poj2706)</li>
</ul>
<h3 id="图算法-1"><a href="#图算法-1" class="headerlink" title="图算法"></a>图算法</h3><ul>
<li>差分约束系统的建立和求解 (poj1201,poj2983)</li>
<li>最小费用最大流 (poj2516,poj2516,poj2195)</li>
<li>双连通分量 (poj2942)</li>
<li>强连通分支及其缩点 (poj2186)</li>
<li>图的割边和割点 (poj3352)</li>
<li>最小割模型、网络流规约 (poj3308)</li>
</ul>
<h3 id="数据结构-1"><a href="#数据结构-1" class="headerlink" title="数据结构"></a>数据结构</h3><ul>
<li>线段树 (poj2528,poj2828,poj2777,poj2886,poj2750)</li>
<li>静态二叉检索树 (poj2482,poj2352)</li>
<li>树状树组 (poj1195,poj3321)</li>
<li>RMQ (poj3264,poj3368)</li>
<li>并查集的高级应用 (poj1703,2492)</li>
<li>KMP算法 (poj1961,poj2406)</li>
</ul>
<h3 id="搜索"><a href="#搜索" class="headerlink" title="搜索"></a>搜索</h3><ul>
<li>最优化剪枝和可行性剪枝</li>
<li>搜索的技巧和优化 (poj3411,poj1724)</li>
<li>记忆化搜索 (poj3373,poj1691)</li>
</ul>
<h3 id="动态规划-1"><a href="#动态规划-1" class="headerlink" title="动态规划"></a>动态规划</h3><ul>
<li>较为复杂的动态规划 (如动态规划解特别的施行商问题等) (poj1191,poj1054,poj3280,poj2029,poj2948,poj1925,poj3034)</li>
<li>记录状态的动态规划 (POJ3254,poj2411,poj1185)</li>
<li>树型动态规划 (poj2057,poj1947,poj2486,poj3140)</li>
</ul>
<h3 id="数学-1"><a href="#数学-1" class="headerlink" title="数学"></a>数学</h3><ul>
<li>组合数学</li>
<li>容斥原理</li>
<li>抽屉原理</li>
<li>置换群与Polya定理(poj1286,poj2409,poj3270,poj1026)</li>
<li>递推关系和母函数</li>
<li>数学</li>
<li>高斯消元法 (poj2947,poj1487, poj2065,poj1166,poj1222)</li>
<li>概率问题 (poj3071,poj3440)</li>
<li>GCD、扩展的欧几里德(中国剩余定理) (poj3101)</li>
<li>计算方法</li>
<li>0/1分数规划 (poj2976)</li>
<li>三分法求解单峰(单谷)的极值</li>
<li>矩阵法 (poj3150,poj3422,poj3070)</li>
<li>迭代逼近 (poj3301)</li>
<li>随机化算法(poj3318,poj2454)</li>
<li>杂题 (poj1870,poj3296,poj3286,poj1095)</li>
</ul>
<h3 id="计算几何学-1"><a href="#计算几何学-1" class="headerlink" title="计算几何学"></a>计算几何学</h3><ul>
<li>坐标离散化</li>
<li>扫描线算法 (例如求矩形的面积和周长并,常和线段树或堆一起使用) (poj1765,poj1177,poj1151,poj3277,poj2280,poj3004)</li>
<li>多边形的内核(半平面交) (poj3130,poj3335)</li>
<li>几何工具的综合应用 (poj1819,poj1066,poj2043,poj3227,poj2165,poj3429)</li>
</ul>
<hr>
<h2 id="高级"><a href="#高级" class="headerlink" title="高级"></a>高级</h2><h3 id="基本算法要求"><a href="#基本算法要求" class="headerlink" title="基本算法要求"></a>基本算法要求</h3><ul>
<li>代码快速写成,精简但不失风格 (poj2525,poj1684,poj1421,poj1048,poj2050,poj3306)</li>
<li>保证正确性和高效性 (poj3434)</li>
</ul>
<h3 id="图算法-2"><a href="#图算法-2" class="headerlink" title="图算法"></a>图算法</h3><ul>
<li>度限制最小生成树和第K最短路 (poj1639)</li>
<li>最短路,最小生成树,二分图,最大流问题的相关理论(主要是模型建立和求解) (poj3155, poj2112,poj1966,poj3281,poj1087,poj2289,poj3216,poj2446</li>
<li>最优比率生成树 (poj2728)</li>
<li>最小树形图 (poj3164)</li>
<li>次小生成树</li>
<li>无向图、有向图的最小环</li>
</ul>
<h3 id="数据结构-2"><a href="#数据结构-2" class="headerlink" title="数据结构"></a>数据结构</h3><ul>
<li>trie图的建立和应用 (poj2778)</li>
<li>LCA和RMQ问题(LCA(最近公共祖先问题)有离线算法(并查集+dfs)和在线算法 (RMQ+dfs)) (poj1330)</li>
<li>双端队列和它的应用(维护一个单调的队列,常常在动态规划中起到优化状态转移的目的) (poj2823)</li>
<li>左偏树(可合并堆)</li>
<li>后缀树(非常有用的数据结构,也是赛区考题的热点) (poj3415,poj3294)</li>
</ul>
<h3 id="搜索-1"><a href="#搜索-1" class="headerlink" title="搜索"></a>搜索</h3><ul>
<li>较麻烦的搜索题目训练 (poj1069,poj3322,poj1475,poj1924,poj2049,poj3426)</li>
<li>广搜的状态优化利用M进制数存储状态、转化为串用hash表判重、按位压缩存储状态、双向广搜、A*算法 (poj1768,poj1184,poj1872,poj1324,poj2046,poj1482)</li>
<li>深搜的优化尽量用位运算、一定要加剪枝、函数参数尽可能少、层数不易过大、可以考虑双向搜索或者是轮换搜索、IDA*算法 (poj3131,poj2870,poj2286)</li>
</ul>
<h3 id="动态规划-2"><a href="#动态规划-2" class="headerlink" title="动态规划"></a>动态规划</h3><ul>
<li>需要用数据结构优化的动态规划 (poj2754,poj3378,poj3017)</li>
<li>四边形不等式理论</li>
<li>较难的状态DP (poj3133)</li>
</ul>
<h3 id="数学-2"><a href="#数学-2" class="headerlink" title="数学"></a>数学</h3><ul>
<li>组合数学</li>
<li>MoBius反演 (poj2888,poj2154)</li>
<li>偏序关系理论</li>
<li>博奕论</li>
<li>极大极小过程 (poj3317,poj1085)</li>
<li>Nim问题</li>
</ul>
<h3 id="计算几何学-2"><a href="#计算几何学-2" class="headerlink" title="计算几何学"></a>计算几何学</h3><ul>
<li>半平面求交 (poj3384,poj2540)</li>
<li>可视图的建立 (poj2966)</li>
<li>点集最小圆覆盖</li>
<li>对踵点(poj2079)</li>
</ul>
<h3 id="综合题"><a href="#综合题" class="headerlink" title="综合题"></a>综合题</h3><ul>
<li>(poj3109,poj1478,poj1462,poj2729,poj2048,poj3336,poj3315,poj2148,poj1263)</li>
</ul>
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